In the first major studies into the magical properties of the complex number and the application to solving the cubic equation, Cardano did the following in around 1539:

He reduced the cubic equation

$ax^3+bx^2+cx+d$

to the form

$x^3=3px+2q$

where $p$ and $q$ are real numbers.

(1). How did Cardano get to this?

There was also another solution to the cubic, discovered before 1926, and it is often referred to as the (del Ferro-)Cardano solution, and is perhaps where Cardano went from in his first reduction. This solution is:

1) To go from the general cubic equation to the normal form one performs the transformation $x = \alpha t+\beta$. A good choice of $\alpha$ and $\beta$ yields $t^3 = 3px + 2q$. One chooses $\alpha$ and $\beta$ so that the other terms drop out.